MATLAB: Finding and Identifying Roots

complexroots

I am attempting to write a code that classifies cubic function as simpler, monotone, or neither. To do this I must calculate the derivative of the cubic function and find its roots. So far the code I have is as follows:
%Solicit Data Needed and Display Data
a = input ('Enter a: ');
b = input ('Enter b: ');
c = input ('Enter c: ');
d = input ('Enter d: ');
fprintf ('Cubic Equation: f(x) = ax^3 + bx^2 + cx + d, a = %10.6f, b = %10.6f, c = %10.6f, d = %10.6f\n', a,b,c,d);
%Give error if a = 0
if a == 0
    error ('Please enter a non-zero value for a!')
end
%Print the Derivative of the cubic function
fprintf ('df/dx = 3ax^2 +2bx +c\n');
%Obtain the Roots of the Derivative
r1 = ((-2*b) + sqrt (((2*b)^2 – (4*3*a*c))/(6*a)));
r2 = ((-2*b) – sqrt (((2*b)^2 – (4*3*a*c))/(6*a)));
fprintf ('The first root of the derivative of f is %10.6f\n' , r1);
fprintf ('The second root of the derivative of f is %10.6f\n' , r2);
The equation for the roots should be correct as I have checked it on my calculator and have double checked all the parenthesis, but for some reason when the program is ran the command window displays the wrong values. I don't know why this is occurring. I also need to identify whether the roots are complex and I cant seem to figure out how to do so. Thanks in advance.
Note: I am at a beginner level and have just recently started learning MATLAB…I may be missing something very obvious.

Best Answer

The parentheses are not correctly placed.
The entire quantity ‘(-2*b) + sqrt((2*b)^2 - (4*3*a*c)))’ should be divided by ‘(6*a)’:
r1 = ((-2*b) + sqrt((2*b)^2 - (4*3*a*c)))/(6*a);
Correct ‘r2’ similarly.
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